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<p>For the system of ODEs</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
\begin{aligned}
\frac{dy}{dt}-\frac{dx}{dt}+y +2x &amp;=&amp;e^t \label{odesys1} \\
\frac{dy}{dt}+\frac{dx}{dt}-x &amp;=&amp;e^{2t} \\
{\rm Initial \ data:} \ \ \ x(0),y(0)&amp;=&amp;1, \label{odesys}
\end{aligned}
\end{equation*}
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